Besides dim regularization, what are the advantages of Euclidean QFT? Initially, I saw Wick rotation as a useful trick to apply dimensional regularization, but then I learned about instantons and how they only exist in Euclidean Yang-Mills.
Also, I heard that path integrals are "more well-defined" in Euclidean spacetime.
What are the other advantages?
 A: It is very good question!
Besides some technical advances, that you already presented in question, first of all, very important to realise statement:

The Osterwalder-Schrader reconstruction theorem states that correla-
tors in a reflection positive Euclidean QFT can be analytically continued
to give Wightman functions that are tempered distributions on Minkowski
space $R^{d−1,1}$.

See, for example, section 3 of Lorentzian methods in conformal field theory
Slava Rychkov. Nowadays, these ideas extensively studied in CFT, see also this. Main idea is very illustrative:

Unitary Lorentzian CFTs are related to reflection-positive Euclidean
CFTs by Wick rotation. This is the Osterwalder-Schrader reconstruction
theorem. Thus, in
principle, everything about a Lorentzian CFT is encoded in the usual CFT
data (operator dimensions and OPE coefficients) that can be studied in
Euclidean signature. However, many observables, and many constraints
on CFT data are deeply hidden in the Euclidean correlators.

Also, it's very important to realise, that Euclidean QFT are used in condensed matter physics. For example, it is useful tool for describing of critical phenomena.For introduction, one can consult
David Tong: Lectures on Statistical Field Theory.
